Making main text flow around the quote is very simple. The basic requirement is a frame for the quote that should be placed above the main text, and then everything should work perfectly. Let's see how.
You have some Text Frames, containing text, and as in this example, set with two columns.
Draw another Text Frame above this one but smaller in size and type the quote inside.
Display the Properties Palette (F2) and go to the Shape tab.
In the Text Flow Around Frame group, click on the Use Frame Shape option.
If you want to set a margin between the quote and the main text, you can set the inner margin of the frame in the Column & Text Distances settings of the PP. By doing this you'll see that the text will have fewer spaces and that the frame will become too small.
You can, alternatively, set the Use Contour Line option of the Shape tab.
Nothing will change right now, but click on the Edit button placed at the top right of the Shape tab. It will...